Old style union and intersection symbols

Question

I find books typeset before 1970 sometimes more comfortable to read than more modern versions. I am trying to get this older book style for some of my LaTeX documents. Thanks to TeX Exchange I get pretty close using the Old Standard font and some adaptations.

The one thing I have been searching for years now is the older set theoretic symbols used by Bourbaki for example. They are "flatter" than the standard ones. Here is an illustration:

Any ideas on how to get such symbols are very welcome!

Answer 1

I'm not sure if I dislike more Bourbaki's mathematical style or the typesetting. Anyway, the symbols at hand are semicircles.

\documentclass[12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{pict2e}
\DeclareFontFamily{U}{matha}{}
\DeclareFontSubstitution{U}{matha}{m}{n}
\DeclareFontShape{U}{matha}{m}{n}{
  <-5.5> matha5
  <5.5-6.5> matha6
  <6.5-6.5> matha7
  <7.5-8.5> matha8
  <8.5-9.5> matha9
  <9.5-11> matha10
  <11-> matha12
}{}
\DeclareSymbolFont{matha}{U}{matha}{m}{n}
\DeclareMathSymbol{\notsign}{\mathrel}{matha}{"7F}
\makeatletter
\DeclareRobustCommand{\flatcap}{\mathbin{\mathpalette\flatcap@\relax}}
\DeclareRobustCommand{\flatcup}{\mathbin{\mathpalette\flatcup@\relax}}
\newcommand{\flatcap@}[2]{%
  \begingroup
  \settowidth{\unitlength}{$\m@th#1\cap$}%
  \begin{picture}(1,0.6)
  \roundcap
  \linethickness{0.075\unitlength}
  \put(0.5,0.1){\arc[0,180]{0.4}}
  \end{picture}%
  \endgroup
}
\newcommand{\flatcup@}[2]{%
  \begingroup
  \settowidth{\unitlength}{$\m@th#1\cap$}%
  \begin{picture}(1,0.6)
  \roundcap
  \linethickness{0.075\unitlength}
  \put(0.5,0.5){\arc[0,-180]{0.4}}
  \end{picture}%
  \endgroup
}
\makeatother
\begin{document}
\itshape
$\mathbf{K}(G,P,B)$ is a partial plane \textup(i.e. $[p,q]\leqq 1$ for $p\notsign= q$\textup) 
if and only if
\begin{equation}
PB\cap BP=P\cup B
\end{equation}
$\mathbf{K}(G,P,B)$ is a partial plane \textup(i.e. $[p,q]\leqq 1$ for $p\notsign= q$\textup) 
if and only if
\begin{equation}
PB\flatcap BP=P\flatcup B
\end{equation}
$\scriptstyle A\flatcup B\flatcap C$
$\scriptstyle A\cup B\cap C$
\end{document}

Note \notsign borrowed from mathabx.

Answer 2

From The Comprehensive LATEX Symbol List, mathabx provides the flattest \cap and \cup, though maybe not flat enough.

\documentclass[12pt]{article}
\usepackage{amsmath,amssymb}
%\usepackage{mathabx}
\DeclareFontFamily{U}{matha}{\hyphenchar\font45}
\DeclareFontShape{U}{matha}{m}{n}{
      <5> <6> <7> <8> <9> <10> gen * matha
      <10.95> matha10 <12> <14.4> <17.28> <20.74> <24.88> matha12
      }{}
\DeclareSymbolFont{matha}{U}{matha}{m}{n}
\DeclareFontSubstitution{U}{matha}{m}{n}
\DeclareMathSymbol{\flatcap}           {2}{matha}{"58}
\DeclareMathSymbol{\flatcup}           {2}{matha}{"59}
\begin{document}
\itshape
$\mathbf{K}(G,P,B)$ is a partial plane (i.e. $[p,q]\leqq 1 \text{ for } p\neq q$) if and only
\begin{equation}
    PB\cap BP=P\cup B
\end{equation}
$\mathbf{K}(G,P,B)$ is a partial plane (i.e. $[p,q]\leqq 1 \text{ for } p\neq q$) if and only
\begin{equation}
    PB\flatcap BP=P\flatcup B
\end{equation}
\end{document}

Answer 3

frown and smile are perhaps closer to the desired form. (I just noticed Sebastiano has a deleted answer saying similar)

\documentclass{article}
\begin{document}
[
PB\cap BP =
PB\frown BP
=
P\cup B =
P\smile B
]
\end{document}